Cartan Triples
Operator Algebras
2020-06-02 v1
Abstract
We introduce the class of Cartan triples as a generalization of the notion of a Cartan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi's theorem to this setting. This context contains that of Fulman's generalization of Cartan MASAs and we discuss his generalization in an appendix.
Cite
@article{arxiv.1810.05267,
title = {Cartan Triples},
author = {Allan P. Donsig and Adam H. Fuller and David R. Pitts},
journal= {arXiv preprint arXiv:1810.05267},
year = {2020}
}
Comments
37 pages